We introduce a framework of electoral competition in which voters have general preferences over candidates' characteristics and policies. Candidates' immutable characteristics (such as gender, race or previously committed policy positions) are exogenously differentiated, while candidates can choose any policy for the remaining issues to maximize their winning probability. Voters have general preferences over the vectors of candidate characteristics and policies, and vote sincerely. Candidates are uncertain about the distribution of voter preferences. We characterize a condition on voter preferences (satisfied in most existing models) under which candidates' equilibrium policies generically converge. In contrast, for voter preferences that violate this condition, we construct a class of models in which policy divergence arises in the unique and strict Nash equilibrium. As a normative criterion, we define competition-efficiency and provide conditions under which the equilibrium is or is not competition-efficient.